PURPOSE: To float a unit and uniformly propagate the twist-back of the unit by forming a curved passage toward a twisting die as a conveying means, and providing many jet holes on the lower face of this passage as air feed passages.

CONSTITUTION: An outer unit 13 guided into a curved passage 32 is floated and run by the spout of the compressed air from many air jet holes 24 provided on a partition plate 31 on the lower face of the curved passage 32 without being brought into contact with the inner face of the partition plate 31 in a curved tube 23, thus the twist-back is uniformly propagated without being disturbed by other objects. When auxiliary rollers 37 are provided at necessary positions, the floating of the outer unit 13 is assisted, the guide is assured, and the necessity for a large compressor to increase the compressed air pressure is reduced even if the unit has a large size. The auxiliary rollers are few in number and have a smaller danger to impair the propagation of the twist-back as compared with roller conveying, and the control is made easier.